Area - squares and rectangles

  • Compare Areas
    problem
    Favourite

    Compare Areas

    Age
    14 to 16
    Challenge level

    Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

  • Pythagoras for a Tetrahedron
    problem
    Favourite

    Pythagoras for a Tetrahedron

    Age
    16 to 18
    Challenge level

    In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of Pythagoras' Theorem.

  • Take a square
    problem

    Take a Square

    Age
    14 to 16
    Challenge level
    Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
  • Paper Halving
    problem

    Paper Halving

    Age
    5 to 11
    Challenge level

    In how many ways can you halve a piece of A4 paper? How do you know they are halves?

  • Lawn Border
    problem

    Lawn Border

    Age
    5 to 11
    Challenge level
    If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
  • Cutting it Out
    problem

    Cutting It Out

    Age
    5 to 11
    Challenge level
    I cut this square into two different shapes. What can you say about the relationship between them?
  • Fit These Shapes
    problem

    Fit These Shapes

    Age
    5 to 11
    Challenge level
    What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
  • Fencing Lambs
    problem

    Fencing Lambs

    Age
    7 to 11
    Challenge level
    A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
  • Great Squares
    problem

    Great Squares

    Age
    7 to 11
    Challenge level
    Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
  • Two Squared
    problem

    Two Squared

    Age
    7 to 11
    Challenge level

    What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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